GNSS Multipath Modeling and Detection in Urban Environment
Shiwen Zhang, Sherman Lo, Yu-Hsuan Chen, Todd Walter, Per Enge, Stanford University
Multipath is a significant source of error in the urban environment and mitigating its effects is vital for numerous GNSS applications such as precise dynamic positioning and high integrity or safety of life. For example, identifying and reducing the effect of multipath allows for high integrity railway control and autonomous vehicle operating near urban environments. This paper examines techniques to manage urban multipath for such environments. The paper examines detection algorithms based on ray tracing and residual checking. It then mates them with processing algorithms based on hard or soft decisions on how to apply the multipath detection results.
This paper describes a satellite exclusion technique that can be applied to land-based or near ground vehicles to reduce Global Positioning System (GPS) position error caused by signal multipath. The proposed technique uses a simplified building model and a ray-tracing algorithm to predict and exclude satellite signals that are corrupted by multipath. The building model ignores detailed structure of roofs and side walls as well as any diffraction and reflection caused by vegetation. A ray-tracing algorithm was implemented to generate prediction for multipath on the building model. The ray-tracing algorithm uses a vector-based approach to search for all possible single reflections from satellite to receiver. The low-complexity of the building model makes it possible to reduce the search space for the ray-tracing algorithm so that the algorithm can be implemented efficiently for simulation. A prediction was generated from simulation to determine whether multipath signal was present given the satellite-receiver geometry. Simulation results show that double and triple reflections are not present in the specific environment. Simulation also shows that range error caused by diffraction is minimal compared to range error from reflected signals. A sensitivity analysis was also performed for the ray-tracing algorithm on the building model. The sensitivity analysis examines how the ray-tracing algorithm performs with modeling uncertainty and error due to model simplification. Independent and identically distributed Gaussian noise was applied to building location and height for each building. A statistical analysis using Monte Carlo simulation was then carried out on the model. Sensitivity analysis describes the confidence level of model prediction under uncertainty.
The following processing algorithm was used for the proposed exclusion technique. The ray-tracing algorithm takes satellite position as input and determines whether multipath is present at the estimated position of the receiver. A confidence level of the model prediction is also generated. The proposed technique only performs satellite exclusion when the model predicts that multipath signal is present with high confidence. This exclusion algorithm is also referred to as the soft decision algorithm. A hard decision algorithm was also implemented for comparison. The hard decision algorithm performs exclusion purely based on model prediction. Additional processing on pseudorange data can also provide information to aid the exclusion decision. Fault detection algorithms based on residual checking will be explored and examined. Checking consistency among pseudorange measurements can make the exclusion technique more robust against modeling error.
Empirical test were performed to examine the performance of the methods analyzed. GPS pseudorange data was collected at different ground locations. Ground truths of testing locations were obtained through Precise Point Positioning (PPP) service. Differential GPS corrections were then applied to pseudoranges to remove ionospheric error and other major range errors. An unweighted least squares algorithm was applied to calculate position solutions. Position accuracy was then evaluated after performing satellite exclusion using the proposed technique. Horizontal Dilution of Precision (HDOP) was also calculated for the proposed technique as another evaluation metric. Results from the proposed technique was compared with results from two other exclusion algorithms: (i) no satellite exclusion, and (ii) hard exclusion.
Simulation and experimental results show that the simplified building model can effectively detect and remove multipath signals especially long-delay multipath. Sensitivity analysis can protect the model from too aggressively removing signals, which leads to worse HDOP and worse position accuracy. Further post-processing work will be done on residual checking to draw additional information for the exclusion technique. Results from model prediction, sensitivity analysis, and residual checking will be compared and weights will be assigned among the three algorithms to make the final decision of satellite exclusion. A weighted least squares algorithm will be implemented to de-weight short-delay multipath signals instead of simple exclusion when HDOP values are high. Multipath characteristics of dual frequency signals will also be explored to aid multipath detection. In severe multipath environment where most signals are corrupted by reflection, multi-constellation will become necessary in order to maintain enough satellites for positioning.